Use of Hilbert transforms to simplify image reconstruction in a spiral scan cone beam CT imaging system

Abstract

A method and apparatus for three dimensional (3D) computerized tomography (CT) imaging wherein a reconstructed image is developed by calculating along line segments L formed in cone beam data. The endpoints of which are determined by a data combination mask. At source positions near the top and bottom of the ROI, the mask is divided into separate portions using a horizontal line, each having a set of line segments L formed therein. The reconstruction data is calculated by performing one-dimensional (1D) convolving operations of the data along the line segments L, the 1D convolving operation developing an additive contribution to a new projection image. Finally, the new projection image is backprojected into a 3D space, thereby reconstructing a 3D image of the ROI in the object.

What is claimed is:  
     
       1. A method for performing three dimensional computerized tomographic imaging a region-of-interest (ROI) in an object using a cone beam source of radiation energy, comprising the steps of: 
       defining a source scan path that encircles the ROI in the object and is traversed by the cone beam source;  
       using the cone beam source, fixed relative to an area detector with both source and as detector movably positioned relative to the object, for applying radiation energy towards the object from a plurality of source positions along the scan path as said source traverses the scan path, said applying causing said area detector to acquire a set of cone beam projection data corresponding to a respective portion of the object at each of said source positions;  
       applying a mask to each set of the acquired projection data so that data inside the boundaries of each mask form a corresponding plurality of masked data sets;  
       calculating image data along each of the line segments L formed in the masked cone beam projection data acquired at each of said source positions, said calculating step comprising performing a plurality of one-dimensional (1D) convolving operations of the masked projection data along a respective group of the line segments L, the 1D convolving operation for each group of the line segments L developing an additive contribution to a new projection image; and  
       3D backprojecting the new projection image into a 3D space, thereby reconstructing a 3D image of the ROI in the object.  
     
     
       2. The method of claim  1 , wherein at source positions near one of a top or bottom edge of the ROI, said mask is divided into separate portions using at least a horizontal line therein, each portion having a group of line segments L formed therein, along which said calculating step performs said convolving operations. 
     
     
       3. The method of claim  1 , wherein the new projection image developed by the convolving operations spreads out the image data over an area greater than the area of the area detector. 
     
     
       4. The method of claim  2 , wherein for masked data sets acquired near one edge of the ROI, a first group of the line segments L comprise a plurality of parallel line segments formed in the masked cone beam data which resides below the horizontal line in the mask. 
     
     
       5. The method of claim  4 , wherein the first group of the line segments L are spatially oriented so as to be parallel to a projection of a tangent to the scan path at the source position which acquired the masked cone beam data set in which the convolving operations for the first group of the line segments L are being performed. 
     
     
       6. The method of claim  4 , wherein for masked data sets acquired near one edge of the ROI, a second group of the line segments L comprise a plurality of parallel line segments L formed in the masked cone beam data which reside above and are spatially oriented so as to be parallel with the horizontal line in the mask. 
     
     
       7. The method of claim  6 , wherein for masked data sets acquired near one edge of the ROI, a third group of the line segments L comprises a plurality of parallel line segments L formed in the masked cone beam data which reside above the horizontal axis in the mask and are spatially oriented so as to be parallel to a projection of a tangent to the scan path at the source position which acquired the masked cone beam data set in which the convolving operations for the third group of the line segments L are being performed. 
     
     
       8. The method of claim  7 , wherein said third group of the line segments L are limited to a portion of the mask residing on one side of a point C 0  on the horizontal line in the mask in which the convolving operations for the third group of the line segments L are being performed. 
     
     
       9. The method of claim  7 , wherein for masked data sets acquired near one edge of the ROI, a fourth group of the line segments L comprises a plurality of radially extending line segments L formed in the masked cone beam data which reside above the horizontal line in the mask and extend radially from or towards a point C 0  on the horizontal line in the mask in which the convolving operations for the fourth group of the line segments L are being performed. 
     
     
       10. The method of claim  2 , including a d/dt processing step for filtering the new backprojection image before said 3D backprojection. 
     
     
       11. The method of claim  1 , wherein said 1D convolving operations comprise Hilbert transformation operations. 
     
     
       12. The method of claim  2 , wherein the line segments L of each group have a consistent spatial orientation with respect to each other, but the spatial orientation of the line segments of at least one group being different from the spatial orientation of the line segments L of another group. 
     
     
       13. The method of claim  2 , wherein said masked cone beam data is divided into separate portions based on the location of a point C 0  determined on an axial line crossing the mask, which point C 0  is defined by an intersection of a projection onto the area detector of the source position which acquired the masked cone beam data and the axial line. 
     
     
       14. The method of claim  13 , wherein the scan path has a longitudinal axis and the point C 0  is determined by: 
       (a) determining a first line ( 406 ) which is tangent to the scan path ( 404 ) and perpendicular to its longitudinal axis;  
       (b) determining a second line ( 410 ) which is parallel to the first line ( 406 ) and which passes through the source position (S i ) which acquired the data being masked; and  
       (c) defining as point C 0  that point where the second line intersects the plane ( 412 ) of the detector.  
     
     
       15. A method for performing three dimensional computerized tomographic imaging near at least one of an upper or lower boundary of a region-of-interest (ROI) in an object using a cone beam source of radiation energy, comprising the steps of; 
       defining a source scan path that encircles the ROI near one of the boundaries in the object and is traversed by the cone beam source;  
       using the cone beam source, fixed relative to an area detector with both source and detector movably positioned relative to the object, for applying radiation energy towards the object from a plurality of source positions along the scan path as said source traverses the scan path, said applying causing said area detector to acquire a set of cone beam projection data corresponding to a respective portion of the object at each of said source positions;  
       applying a mask to each set of the acquired projection data so that data inside each mask form a corresponding plurality of masked data sets;  
       dividing those masked data sets acquired near a boundary of the ROI into a plurality of different spatial regions, one or more of said regions including a set of line segments L formed in the masked data which have a consistent spatial orientation with respect to each other, but with the line segments L of one region having a different spatial orientation with respect to the line segments L of another region;  
       calculating image data along each of the line segments L formed in the masked cone beam projection data acquired at each of said source positions, said image data corresponding to an additive contribution to a new projection image; and  
       3D backprojecting the new projection image into a 3D space, thereby reconstructing a 3D image of the ROI in the object.  
     
     
       16. The method of claim  15 , wherein said calculating step comprises performing a plurality of one-dimensional (1D) convolving operations of the masked projection data along a respective group of the line segments L, the 1D convolving operation for each group of the line segments L developing the additive contribution to a new projection image. 
     
     
       17. The method of claim  16 , wherein said 1D convolving operations comprise Hilbert transformation operations. 
     
     
       18. A method for performing three dimensional computerized tomographic imaging near a boundary of a region-of-interest (ROI) in an object using a cone beam source of radiation energy, comprising the steps of: 
       defining a source scan path that encircles the ROI in the object and is traversed by the cone beam source;  
       using the cone beam source, fixed relative to an area detector with both source and detector movably positioned relative to the object, for applying radiation energy towards the object from a plurality of source positions along the scan path as said source traverses the scan path, said applying causing said area detector to acquire a set of cone beam projection data corresponding to a respective portion of the object at each of said source positions;  
       applying a mask to each set of the acquired projection data so that data inside the boundaries of each mask form a corresponding plurality of masked data sets;  
       dividing those masked data sets acquired near a boundary of the ROI into a plurality of different spatial regions, one or more of said regions including a set of line segments L formed in the masked data which have a consistent spatial orientation with respect to each other, but with the line segments L of one region having a different spatial orientation with respect to the line segments L of another region;  
       calculating image data along each of said line segments L for developing an additive contribution to a new projection image; and  
       3D backprojecting the new projection image into a 3D space, thereby accurately reconstructing a 3D image of the boundary of the ROI in the object.  
     
     
       19. Apparatus for performing three dimensional computerized tomographic imaging near a boundary of a region-of-interest (ROI) in an object using a cone beam source of radiation energy, comprising: 
       a source of cone beam radiation energy;  
       a manipulator for providing a source scanning trajectory as a scan path that encircles the ROI in the object and causes the source and detector to traverse the scan path;  
       means for causing the source to apply radiation energy towards the object from a plurality of source positions along the scan path as said source traverses the scan path, said area detector acquiring cone beam projection data corresponding to respective portions of the object at each of said source positions; and  
       an image reconstruction processor for,  
       applying a mask to the cone beam projection data acquired at each of said source positions,  
       dividing those masked data sets acquired near a boundary of the ROI into a plurality of different spatial regions, at least two of said regions each including a set of line segments L formed therein which have a consistent spatial direction relative to each other, wherein the spatial direction of the line segments L of one region are different from the spatial direction of the line segments L of another region;  
       calculating image data along each of said line segments L for developing an additive contribution to a new projection image; and  
       3D backprojecting the new projection image into a 3D space, thereby accurately reconstructing a 3D image of the boundary of the ROI in the object.  
     
     
       20. The apparatus of claim  19 , wherein said image reconstruction processor calculates a plurality of one-dimensional (1D) convolving operations of the masked projection data along a respective group of the line segments L, the 1D convolving operation for each group of the line segments L developing the additive contribution to a new projection image. 
     
     
       21. The apparatus of claim  20 , wherein said image reconstruction processor performs Hilbert transformation operations as said 1D convolving operations.